By ``structured" the authors mean ``tridiagonal" (and/or, in
principle, also semiseparable) and by ``matrices" the authors mean
``real symmetric matrices". In the context of QR methods their
motivation and challenge originates from the well known loss of
orthogonality of computed eigenvectors if the spectrum is
``clustered". They offer a method designed to be much less costly
than the ``natural" Gramm-Schmidt procedure. Its key idea is that
for structured matrices the single step of the QR method leaves
the factors still ``highly structured" (i.e., for example, upper
Hessenberg and semiseparable in the tridiagonal case). A tabulated
menu of six numerical examples offers an illustration to be
enjoyed by the specialists.

MR2202999 Mastronardi, N.; Van Barel, M.; Van Camp, E.; Vandebril,
R. On computing the eigenvectors of a class of structured
matrices. J. Comput. Appl. Math. 189 (2006), no. 1-2, 580--591.
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